You've had good advice, especially the "ride fast" -- honestly, going fast enough to generate heat is what makes most difference for me. I can't do wool (allergies) so I layer up, and when it's the nastiest -- cold *and* wet -- then I make sure I"m wearing the higher-tech stuff. I've got two layers of gloves and duckboots for when it's really wet (but I'm shopping for something better for the feet).
I don't have a "drying cupboard," but I've got a computer under my desk and can drape at least one thign where it will dry without shorting things out... and I'll bring along spares. Makes for lots of laundry, though.